Propeller-Wing Interaction: A Simplified Method for Coupling BEM and CFD

This paper presents a numerical procedure for studying the interaction between the wake generated by a propeller and the wing, considering a tiltrotor model framed within the T-TECH Italian project, which has the scope to develop innovative technologies for a flight demonstrator. A tiltrotor is an aircraft that generates lift and propulsion by way of powered rotors mounted on rotating shafts or nacelles at the ends of a fixed wing; in which, in contrast with conventional aircraft, the dimension of the propeller is comparable with the vehicle one. The procedure proposes to couple a 3D low-order unsteady Boundary Element Method (BEM) approach, to evaluate the performance of the isolated propeller, and a Reynolds-Averaged Navier-Stokes (RANS) solution for the analysis of the flow field interaction between the propeller (simulated as actuator disk) and the wing.


Introduction
This paper is devoted to present the results of the application of a BEM/RANS coupled procedure for the characterization of the flow field for a tiltrotor [1] in airplane and helicopter modes.These modes depend on the angle between the axis of the propeller and wing plane, and they are respectively used in cruise and take off / landing.For vertical flight, the rotation axis of the rotors is vertical to generate lift, while for airplane mode, the rotors are angled forward, generating thrust.The modes are reported in Figure 1.In helicopter mode, two moving surfaces are deflected to reduce the normal force on the wing (Figure 2).The outer surface is the flaperon, which is used as flight control surface, and the inner one is the morphing surface, which is typical of the tiltrotor vehicle and may be angled up to 90°.The proposed procedure allows to achieve high-fidelity results regarding the analysis of the wake interaction between the propeller and the wing, simplifying the simulation in the tiltrotor airplane mode, since current studies focused on the propeller-wing interaction show a lot of complexities: performing a full CFD analysis for both components may cause problems in terms of boundary and interface settings, fidelity of results, and time-consuming simulations [2].Moreover, since we are referring to a non-conventional configuration, characterized by the presence of a big propeller compared to the dimension of the wing, the CFD approach could result very complex to set-up [3].In addition, the procedure makes the simulation accessible in helicopter mode with hovering condition, because a BEM solver cannot be used in this mode, as the pressure on the lower side of the wing is unknown, and an unsteady CFD analysis should be performed.The next sections are organized as follows: Section 2 is devoted to the numerical validation of BEM software for the isolated propeller; Section 3 includes the description of the BEM/RANS procedure; in Section 4 the BEM/RANS procedure is employed in the airplane mode case and compared with BEM results; Section 5 reports the results for the helicopter mode in hovering with BEM/RANS procedure and Section 6 has the conclusions and the future development.

Validation of BEM solver
The BEM software validation was performed for the isolated propeller through experimental data of the Bell XV-15 aircraft, available from Bell [4] for the airplane mode and from Felker [5] (OARF experiments) and Bartie [6] (WPAFB experiments) for the helicopter mode.The propeller choice depends on the amount of publicly available information and the similarities with the blade of the T-TECH aircraft, which is generative of the Bell one.The comparison was conducted in terms of isolated propeller thrust for airplane and helicopter modes; eventually, a comparison with RANS results was even done.

Airplane Mode
For the airplane mode, three analyses were performed with different collective pitch angles, which varied around the operational one (38.9°-40°).The variation between the experimental results of literature [4] and those obtained through the BEM software is lower than 7.5% (Table 1).

Helicopter Mode
For the helicopter mode three analyses were conducted by varying the collective pitch (5° -15°).The experimental and BEM results are reported in Figure 3 in terms of thrust coefficient (  ).Even in this mode, the variation is lower than 5%.Finally, the propeller blade was used for a RANS analysis in order to compare the pressure distribution for different sections of the blade, verifying the results detail on the surface of blades, like the overall result in terms of thrust.The trends of the pressure coefficient for two sections of the blade are reported in Figure 4.After validating the code, we proceed in the following sections with the description of the procedure and results.

BEM/RANS Procedure
The starting point of the BEM/RANS procedure is represented by the geometry of the propeller: the in-house BEM software PaMs [7] is used to evaluate the normal and tangential forces on blades sections along the radius.Using the Blade Element Theory [8] the characteristics curves of the propeller based on BEM solution are evaluated (i.e., dC T dr ⁄ and dC Q dr ⁄ ).These quantities are used to perform a RANS simulation by introducing the actuator disk model [9] according to the general momentum theory, in which pressure drop and tangential components of the propeller wake are modeled.In Figure 5 the procedure is schematically reported.

Airplane Mode Analyses
This section analyzes the airplane mode configuration through an unsteady full BEM analysis.Subsequently, the BEM/RANS procedure is performed and both results are compared.

Unsteady BEM Analysis
Since the analysis performed by the BEM code is unsteady, it is possible to appreciate the timedependent effect of the wing on the propeller, and vice versa.The first effect is due to two contributions: the wing thickness (effective upwash) and the wing circulation (upwash on the lower side of the wing and downwash on the upper side) (Figure 6).The results of these analyses are plotted in Figure 7: the vertical axis represents the normal force coefficient in a specific section of the blade (r/R=0.7); the horizontal axis represents the azimuth angle of the blade (Azimuth=270° corresponds to the angle where the blade is in the same plane of the wing).The isolated propeller returns a constant value; the propeller + wing with zero lift has only the contribution of wing thickness, which affects as an upwash on the blades, returning an increase of the normal force coefficient; the "propeller + wing" case has the wing thickness and circulation contributions, showing an oscillation in the normal force coefficient on the blade at 270°.The effect of the blade on the propeller is mainly caused by the blade downwash, which affects as upwash on the wing (Figure 8) Figure 8.A schematic of the mechanism of the proprotor effect on the wing [10].
In this case, the lift coefficient in a section of the wing (2y/b=0.52) is plotted against the azimuth of the propeller in Figure 9.The lift coefficient has 3 spikes, corresponding to the passage of the blades in the wing plane.

BEM/RANS Procedure and Comparison with BEM results
After performing the airplane mode through the BEM solver, the BEM/RANS procedure is employed in the airplane mode, Figure 10 reports the contour of velocity and pressure at 60% of the wingspan.The pressure coefficient distribution for both cases is similar, and even the lift coefficient of whole wing differences of less than 1%.

Helicopter Mode Analyses
The helicopter mode cannot be analyzed through a BEM solver; hence, a RANS solver has to be used and the BEM/RANS procedure can simplify the analysis.Two configurations of the tiltrotor are performed, considering the moving surfaces deflected and non-deflected.Figure 12 and Figure 13 report the contour of pressure and velocity at 60% of the wingspan for both configurations.The contours of pressure show how the deflection of moving surfaces induces a decrease of pressure on the wing upper side, reducing the normal force by roughly 46%.

Conclusions and Future Development
The BEM/RANS procedure proposed in this paper is a simplified method which has the aim to achieve high-fidelity results regarding the analysis of the wake interaction between the propeller and the wing, simplifying the analysis and reducing the simulation time-consuming, without physically modeling the propeller in the RANS solver.It achieves the propeller performance via BEM analysis and introduces the actuator disk model for the propeller characterization in a RANS solver (Section 3).
After validating the BEM solver for the isolated propeller with the experimental data of Bell XV-15 (Section 2), the BEM/RANS procedure was first employed in the airplane mode configuration of a tiltrotor vehicle and the results were compared with the BEM ones with a good correlation (Figure 11).Afterward, the procedure was performed for the helicopter mode, where the BEM software cannot be used for the full analysis.Two configurations of tiltrotor have been compared: with and without the moving surfaces deflected (Section 5).
For future development of this methodology, other flight modes may be considered, such as the conversion mode, and the upwash/downwash effect of the wing on the propeller may be even considered in the RANS solver, introducing a correction of the propeller performance depending on it.

Figure 1 .
Figure 1.Schematic representation of airplane mode (a) and conversion mode (b) for the tiltrotor vehicle.

Figure 2 .
Figure 2. The geometry of tiltrotor in helicopter mode with moving surfaces deflected: Morphing and Flaperon.

Figure 3 .
Figure 3. Helicopter Mode: Comparison of PaMs results with experimental for the Bell XV-15 aircraft.

Figure 5 .
Figure 5.A schematic representation of the workflow for the BEM/RANS procedure.

Figure 6 .
Figure 6.A schematic of the mechanism of the wing effect on the propeller [10].

Figure 7 .
Figure 7. Normal force coefficient vs azimuth angle of the blade in a section at 70% of the radius, for three cases: Propeller + Wing (Black); Isolated Propeller (Blue); Propeller + Wing Zero Lift (Red).

Figure 11
Figure11reports the pressure coefficient distribution along the nondimensional chord for the wing section at 20% and 60% for the BEM and RANS solution.

Figure 11 .
Figure 11.Comparison of BEM-RANS results for the pressure coefficient along the nondimensional chord in two wing sections: 20% and 60% of wingspan.

Table 1 .
Airplane Mode: Comparison of PaMs results with experimental data for the Bell XV-15 propeller.